A multiscale method for compressible liquid-vapor flow with surface tension^*

¹ Institut für Aerodynamik and Gasdynamik, Universität Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart, Germany ;
e-mail: Felix.Jaegle@iag.uni-stuttgart.de
² Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany ;
e-mail: Christian.Rohde@mathematik.uni-stuttgart.de, Christoph.Zeiler@mathematik.uni-stuttgart.de

Abstract

Discontinuous Galerkin methods have become a powerful tool for approximating the solution of compressible flow problems. Their direct use for two-phase flow problems with phase transformation is not straightforward because this type of flows requires a detailed tracking of the phase front. We consider the fronts in this contribution as sharp interfaces and propose a novel multiscale approach. It combines an efficient high-order Discontinuous Galerkin solver for the computation in the bulk phases on the macro-scale with the use of a generalized Riemann solver on the micro-scale. The Riemann solver takes into account the effects of moderate surface tension via the curvature of the sharp interface as well as phase transformation.

First numerical experiments in three space dimensions underline the overall performance of the method.